Nonadditivity in loglinear models using ϕ-divergences and MϕEs under product-multinomial sampling

Based on ϕ-divergence measures and minimum ϕ-divergence estimators (MϕEs), we present three families of test statistics for testing nonadditivity in loglinear models. The minimum ϕ-divergence estimator can be seen to be a generalization of the maximum likelihood estimator. In the process of testing nonadditivity, the two-stage tests procedure is usually used as the standard method. The unknown parameters are first estimated by some method (here MϕEs) and then these estimators which are treated as known constants are applied in the second-stage of this procedure. These three families of statistics which generalize the conclusions in Pardo and Pardo (2005) are asymptotically chi-squared. In the last section, we apply our method to a practical example and do a simulation study.